迷向表示分为6个不可约直和的旗流形上不变爱因斯坦度量  

Invariant Einstein Metrics on Some Generalized Flag Manifolds with Six Isotropy Summands

作　　者：王瑜 秦华军 赵国松[3] WANG Yu;QIN Huajun;ZHAO Guosong(Corresponding author. Department of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, China;Department of Mathematics, Sichuan Normal University, Chengdu 610068,China;Department of Mathematics, Sichuan University, Chengdu 610064, China)

机构地区：[1]四川轻化工大学数学与统计学院,四川自贡643000 [2]四川师范大学数学学院,成都610068 [3]四川大学数学学院,成都610064

出　　处：《数学年刊（A辑）》2019年第3期259-286,共28页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11501390,No.11726608,No.11571242);四川省科技厅项目(No.2019YJ0456,No.2016JQ0046)的资助

摘　　要：众所周知,计算广义旗流形G/K上不变爱因斯坦度量存在两个困难:(1)如何计算旗流形的非零结构常数;(2)如何计算旗流形爱因斯坦方程组的Grobner基.在这篇文章中用定理2.1来计算旗流形的非零结构常数,用Maple软件来计算旗流形爱因斯坦方程组的Grobnexr基.最后得到旗流形F4/U^2(1)×SU(3),E6/U^2(1)×SU(3)×SU(3),E7/U^2(1)×SU(2)×SU(5),E7/U^2(1)×SU(6),E7/U^2(1)×SU(2)×SO(8)与E8/U^2(1)×E6上爱因斯坦度量.There are two difficulties to obtain invariant Einstein metrics on generalized flag manifolds G/K,one is how to compute non-zero structure constants of the flag manifolds,the other is how to compute Grolbner bases of the system of the Einstein equations.In this paper,the authors compute non-zero structure constants by the method given in Theorem2.1,and get Grobner bases of the system of the Einstein equations by using the software Maple.In this way the authors obtain invariant Einstein metrics on the flag manifolds F4/U^2(1)×SU(3),E6/U^2(1)×SU(3)×SU(3),E7/U^2(1)×SU(2)×SU(5),E7/U^2(1)×SU(6),E7/U^2(1)×SU(2)×SO(8)and E8/U^2(1)×E6 respectively.

关 键 词：齐性空间 广义旗流形 MAPLE软件 迷向表示 爱因斯坦度量 等距 

分 类 号：O186.12[理学—数学]